Find the derivative $\frac{d}{dx}\left(\ln\left(\mathrm{sinh}\left(\pi x\right)\right)+\sin\left(\ln\left(x\right)\right)\right)$ using the sum rule

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(ln(sinh(pix))+sin(ln(x))) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}.